The width of the figure below is 5 units. The perimeter of the figure is 18 units. What is the length of the figure in units?

Mathematics

1 answer:

marishachu [46]3 years ago

3 0

if the figures perimeter is 18 units, and the width of the figure is 5 units. I am guessing the figure is a rectangle

where the width is 5 units, and 2 of the sides have 2 be the same 2 be a rectangle, than the width on each side is 10 units all together

18-10= 8

if the figure is a rectangle then that means there are 2 sides left of equal length so if we divide our current number (8) by 2 then we will have the length of each side (4)

8 divided by 2= 4

width= 5

length= 4

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Let us use a simple diagram to interprete the question

In the diagram above, the dark stuff below represents the shadow and the rectangular bar represents the building. I have labelled the height of the building as h.

So we will use the right-angled triangle formed to find h

As we can see h represents the opposite side and 56.5 feet represents the adjacent side of the right-angle triangle. So we will use TOA

$\text{TOA tan }\theta=\frac{opposite}{\text{adjacent}}$

So we have

$\begin{gathered} \text{ tan }\theta=\frac{opposite}{\text{adjacent}} \\ \text{ tan }61.7\degree=\frac{h}{56.5} \\ 1.8572015=\frac{h}{56.5} \\ \text{cross multiplying, we have } \\ h=1.8572015\times56.5 \\ h=104.931887 \end{gathered}$

Hence the answer is 104.9 feet to the nearest tenth